Vibrational Coupled Cluster Method Research Articles

Effect of vibrational resonances and dynamic polarizability on the Raman spectrum of furfural: A vibrational coupled cluster study

The Raman spectrum of furfural is computed and analyzed using the Vibrational Coupled Cluster Method (VCCM). Furfural has immense applications in organic synthesis, electrocatalysis and energy conversion process. The experimental Raman spectrum of furfural is congested and broad, even in the medium energy regions like C-C stretching and CO stretching regions. We extensively analyze the Fermi and higher quanta resonance effects on the Raman spectrum by examining the VCCM wavefunctions. In addition, a systematic study on the effect of incident frequency on the anharmonic Raman activity is carried out by comparing the results with incident wavelengths 325.0 nm and 632.8 nm against static polarizability.

An approximation to the vibrational coupled-cluster method for CH-stretching of large molecules: application to naphthalene and anthracene.

We propose an approximation to the vibrational coupled-cluster method (VCCM) to describe the CH-stretching region of the vibrational spectrum of large molecules. The vibrational modes of a molecule are divided into two sets: the target set and the bath set. The target set includes the CH stretches and the modes that are strongly coupled with the CH stretches and/or involve strong Fermi resonances with a CH stretch fundamental. The rest of the modes are in the bath set. First, the effective harmonic oscillator (EHO) approximation is invoked for the whole system to obtain the zeroth-order frequencies and modified potentials. The effects of interaction between the bath set and the target sets are included in the modified potential from the EHO calculation. The VCCM equations are constructed with the modified potential from the EHO calculations and for the target set only. The transition energies and intensities are calculated using such a truncated VCCM approximation. The proposed method is applied to calculate the IR spectra of naphthalene and anthracene. The results with three different criteria for selecting the modes in the target set are compared with the experimental IR spectra.

Systematic and variational truncation of the configuration space in the multiconfiguration time-dependent Hartree method: The MCTDH[n] hierarchy.

The multiconfiguration time-dependent Hartree (MCTDH) method is a powerful method for solving the time-dependent Schrödinger equation in quantum molecular dynamics. It is, however, hampered by the so-called curse of dimensionality which results in exponential scaling with respect to the number of degrees of freedom in the system and, thus, limits its applicability to small- and medium-sized molecules. To avoid this scaling, we derive equations of motion for a series of truncated MCTDH methods using a many-mode second-quantization formulation where the configuration space is restricted based on mode-combination levels as also done in the vibrational configuration interaction and vibrational coupled cluster methods for solving the time-independent Schrödinger equation. The full MCTDH wave function is invariant with respect to the choice of constraint (or gauge) operators, but restricting the configuration space removes this invariance. We, thus, analyze the remaining redundancies and derive equations for variationally optimizing the non-redundant matrix elements of the constraint operators. As an alternative, we also present a constraint that keeps the density matrices block diagonal during the propagation and the two choices are compared. Example calculations are performed on formyl fluoride and a series of high-dimensional Henon-Heiles potentials. The results show that the MCTDH[n] methods can be applied to large systems and that an optimal choice of constraint operators is key to obtaining the correct physical behavior of the wave function.

Lowest order perturbative approximation to vibrational coupled cluster method in bosonic representation

We propose a perturbative approximation to the vibrational coupled cluster method in bosonic representation to reduce the cost of calculating the cluster matrix elements by considering only the first order of S and $$\sigma $$ for the construction of the effective Hamiltonian $$e^\sigma e^{-S}He^Se^{-\sigma }$$ . With the systematic analysis of the results of two molecules, $$\hbox {H}_2\hbox {O}$$ and 1,1-difluoroethylene, we find that the accuracy of the transition energies with such low order approximation is comparable to the fully converged VCCM. The lowest order perturbative approximation is used to calculate the cluster matrix elements of the vibrational coupled cluster method in bosonic representation. The computational scaling for cluster matric elements is reduced from iterative N6 to non-iterative N4.

Tensor-decomposed vibrational coupled-cluster theory: Enabling large-scale, highly accurate vibrational-structure calculations.

A new implementation of vibrational coupled-cluster (VCC) theory is presented, where all amplitude tensors are represented in the canonical polyadic (CP) format. The CP-VCC algorithm solves the non-linear VCC equations without ever constructing the amplitudes or error vectors in full dimension but still formally includes the full parameter space of the VCC[n] model in question resulting in the same vibrational energies as the conventional method. In a previous publication, we have described the non-linear-equation solver for CP-VCC calculations. In this work, we discuss the general algorithm for evaluating VCC error vectors in CP format including the rank-reduction methods used during the summation of the many terms in the VCC amplitude equations. Benchmark calculations for studying the computational scaling and memory usage of the CP-VCC algorithm are performed on a set of molecules including thiadiazole and an array of polycyclic aromatic hydrocarbons. The results show that the reduced scaling and memory requirements of the CP-VCC algorithm allows for performing high-order VCC calculations on systems with up to 66 vibrational modes (anthracene), which indeed are not possible using the conventional VCC method. This paves the way for obtaining highly accurate vibrational spectra and properties of larger molecules.

Performance of different density functionals for the calculation of vibrational frequencies with vibrational coupled cluster method in bosonic representation

An accurate description of anharmonic vibrational frequencies of polyatomic molecules is a challenging task. It requires an ab initio method to solve the vibrational Schrodinger equation along with extensive electronic structure calculations to generate the quartic potential energy surface (PES) in mass-weighted normal coordinates. The computation of such quartic PES is very expensive. Even for a medium-size molecule, highly accurate ab initio methods like CCSD, CCSD(T) become formidable. The DFT stands as valuable alternative in this case. In this work, we investigate the performances of several commonly used density functionals, namely, B3LYP, BLYP, B3LYPD, M06, M062x, PBE1PBE, B3P86, LC- $$\omega $$ PBE, X3LYP, B3PW91, and B97D for the evaluation of anharmonic vibrational frequencies of semi-rigid molecules. The quality of the results is assessed by the comparison with experimental values. To this end, we used a set of 19 molecules of various sizes (4–9 atoms). The vibrational coupled cluster method (VCCM) in bosonic representation is used to solve the vibrational structure problem. The hybrid functionals B3P86, B3LYP, B3PW91, PBE1PBE, and X3LYP found to give more accurate result of the fundamental frequencies than the other functionals. Our results show that the error in the BLYP and B97D calculation is due to the inadequate description of the harmonic force field. For the LC- $$\omega $$ PBE, M06, and M062x, the anharmonic force constants leads to the error. It is found that the comparative performances of the DFT functionals with VCCM are consistent with the second-order vibrational perturbation theory.

Raman spectral calculation by vibrational coupled-cluster method in bosonic representation

ABSTRACTWe present a method to calculate the Raman spectra of poly-atomic molecules using the vibrational coupled-cluster method in bosonic representation. The effective operator-based approach with Arponen's extended coupled-cluster ansatz is used to calculate the transition matrix elements associated with the polarisability surface to calculate the Raman intensities. A test calculation is made on furan and the resultant spectrum is compared with the experimental spectrum. The agreement between the theoretical anharmonic spectrum and experimental spectrum is quite good. An observation made from these calculations is that the transitions in the 3000–3200 cm−1 range (CH stretch) is dominated by several transitions to final states that are dominated by multiple quantum states and hardly to any single fundamental state. We used both dynamic and static polarisabilities and found that the spectra generated from these two polarisability tensors are practically identical, implying that the polarisability tensor is insensitive to the incident frequency.

Approximate inclusion of four-mode couplings in vibrational coupled-cluster theory

The vibrational coupled cluster (VCC) equations are analyzed in terms of vibrational Mo̸ller-Plesset perturbation theory aiming specifically at the importance of four-mode couplings. Based on this analysis, new VCC methods are derived for the calculation of anharmonic vibrational energies and vibrational spectra using vibrational coupled cluster response theory. It is shown how the effect of four-mode coupling and excitations can be efficiently and accurately described using approximations for their inclusion. Two closely related approaches are suggested. The computational scaling of the so-called VCC[3pt4F] method is not higher than the fifth power in the number of vibrational degrees of freedom when up to four-mode coupling terms are present in the Hamiltonian and only fourth order when only up to three-mode couplings are present. With a further approximation, one obtains the VCC[3pt4] model which is shown to scale with at most the fourth power in the number of vibrational degrees of freedom for Hamiltonians with both three- and four-mode coupling levels, while sharing the most important characteristics with VCC[3pt4F]. Sample calculations reported for selected tetra-atomic molecules as well as the larger dioxirane and ethylene oxide molecules support that the new models are accurate and useful.

Computation of expectation values from vibrational coupled-cluster at the two-mode coupling level

In this work we show how the vibrational coupled-cluster method at the two-mode coupling level can be used to calculate zero-point vibrational averages of properties. A technique is presented, where any expectation value can be calculated using a single set of Lagrangian multipliers computed solving iteratively a single linear set of equations. Sample calculations are presented which show that the resulting algorithm scales only with the third power of the number of modes, therefore making large systems accessible. Moreover, we present applications to water, pyrrole, and para-nitroaniline.

Calculation of Dipole Transition Matrix Elements and Expectation Values by Vibrational Coupled Cluster Method.

An effective operator approach based on the coupled cluster method is described and applied to calculate vibrational expectation values and absolute transition matrix elements. Coupled cluster linear response theory (CCLRT) is used to calculate excited states. The convergence pattern of these properties with the rank of the excitation operator is studied. The method is applied to a water molecule. Arponen-type double similarity transformation in extended coupled cluster (ECCM) framework is also used to generate an effective operator, and the convergence pattern of these properties is compared to the normal coupled cluster (NCCM) approach. It is found that the coupled cluster method provides an accurate description of these quantities for low lying vibrational excited states. The ECCM provides a significant improvement for the calculation of the transition matrix elements.

First-principles theories for anharmonic lattice vibrations

Size-extensive generalizations of the vibrational self-consistent field (VSCF), vibrational Moller-Plesset perturbation (VMP), and vibrational coupled-cluster (VCC) methods are made to anharmonic lattice vibrations of extended periodic systems on the basis of a quartic force field (QFF) in delocalized normal coordinates. Copious terms in the formalisms of VSCF that have nonphysical size dependence are identified algebraically and eliminated, leading to compact and strictly size-extensive equations. This "quartic" VSCF method (qVSCF) thus defined has no contributions from cubic force constants and alters only the transition energies of the underlying harmonic-oscillator reference from a subset of quartic force constants. It also provides a way to evaluate an anharmonic correction to the lattice structure due to cubic force constants of a certain type. The second-order VMP and VCC methods in the QFF based on the qVSCF reference are shown to account for anharmonic effects due to all cubic and quartic force constants in a size-extensive fashion. These methods can be readily extended to a higher-order truncated Taylor expansion of a potential energy surface in normal coordinates. An algebraic proof of the lack of size-extensivity in the vibrational configuration-interaction method is also presented.

Vibrational coupled cluster theory.

The theory and first implementation of a vibrational coupled cluster (VCC) method for calculations of the vibrational structure of molecules is presented. Different methods for introducing approximate VCC methods are discussed including truncation according to a maximum number of simultaneous mode excitations as well as an interaction space order concept is introduced. The theory is tested on calculation of anharmonic frequencies for a three-mode model system and a formaldehyde quartic force field. The VCC method is compared to vibrational self-consistent-field, vibrational Møller-Plesset perturbation theory, and vibrational configuration interaction (VCI). A VCC calculation typically gives higher accuracy than a corresponding VCI calculation with the same number of parameters and the same formal operation count.

A second quantization formulation of multimode dynamics.

A new formalism for calculating and analyzing many-mode quantum dynamics is presented. The formalism is similar in spirit to the second quantization formulation of electronic structure theory. The similarity means that similar techniques can be employed for calculating the many-mode nuclear wave function. As a consequence a new formulation of the vibrational self-consistent-field (VSCF) method can be developed. Another result is that the formalism opens up for the construction of new methods that go beyond the VSCF level. A vibrational coupled cluster (VCC) theory is constructed using the new formalism. The size-extensivity concept is introduced in the context of multimode wave functions and the size extensivity of approximate VCC methods is illustrated in comparison with the non-size-extensive vibrational configuration interaction method.